Introduction to Philosophy Philosophy 110W Spring 2013 Russell Marcus

Size: px
Start display at page:

Download "Introduction to Philosophy Philosophy 110W Spring 2013 Russell Marcus"

Transcription

1 Introduction to Philosophy Philosophy 110W Spring 2013 Russell Marcus Class #10: October 1 Smart, The Tenseless Theory of Time aka the B-Theory Marcus, Introduction to Philosophy, Slide 1

2 The Presentist A-Theory P Zimmerman relied on his intuitions about the importance of the present contrasted with past and future events and objects. Thank goodness that s over. P When some thing or event passes from the present into the past, we ordinarily believe that it disappears. It becomes unreal. We lose it. P Yesterday s breakfast P Next Thursday s dinner P These words Marcus, Introduction to Philosophy, Slide 2

3 Intuition and Philosophy P Appeals to intuition are controversial. P Smart prefers scientific evidence to intuitive evidence. More strongly: the only evidence is scientific evidence. P The most fundamental scientific theories are best understood tenselessly. Mathematics contains no references to time. Physics takes time as a variable, but prefers no particular time. The physical laws are indifferent to the direction of time. P Physical theory makes no reference to the present or the past or the future. P I ll say more about intuition if we have time, later. Marcus, Introduction to Philosophy, Slide 3

4 Tenseless Time P Smart argues that we should prefer a theory of time which is tenseless. P The tenseless and minimally token-reflexive language enables us to see the world, in Spinoza s phrase, sub specie aeternitatis (Smart 101). Marcus, Introduction to Philosophy, Slide 4

5 Three Tensed Sentences 1. Bonnie bopped Bobby at 4pm yesterday. 2. Bonnie is bopping Bobby right now. 3. Bonnie will bop Bobby tomorrow at noon. P Zimmerman: these events have intrinsic temporal properties. P Smart: these events have only relational temporal properties. Marcus, Introduction to Philosophy, Slide 5

6 Reichenbach and the Token-Reflexive Solution TR1. There is a time t such that Bonnie bops Bobby at t and t is earlier than the utterance of 1 (by some measure of temporal distance between 4pm yesterday and the utterance of 1, in arbitrary units). TR2. Bonnie bops Bobby simultaneously with the utterance of 1. TR3. There is a time t, such that Bonnie bops Bobby at t, and t is later than the utterance of 3 (by some measure of temporal distance between the utterance of 3 and noon tomorrow, in arbitrary units). P All references to time are rendered in terms of earlier than, and simultaneous with. We can also invoke later than. P No uses of past, present, or future are required for the characterization of times. Marcus, Introduction to Philosophy, Slide 6

7 Tenseless Verbs P No uses of tenses, other than the present tense, are used by the tenseless theory. P Present-tense verbs are to be understood tenselessly. We are taking a four-dimensional view. The block theory P We need, from a grammatical standpoint, some tenses for our verbs. P We think of them as mere grammatical artifacts. Verbs are grammatically present-tense, but logically tenseless. When we say that two plus two equals four we do not mean that two plus two equals four at the present moment. Nor do we mean that two plus two always equaled four in the past, equals four now, and will always equal four in the future (94-5). Marcus, Introduction to Philosophy, Slide 7

8 The Block Theory P Smart is urging a four-dimensional view. Not to be confused with the A-theorist s growing-block theory. P There is a static block, the entire temporal history of the world, past through future. P We can imagine ourselves peering from apart at that block, describing all that happens within it. P The block theory underlies time-travel fiction. Moving among different portions of the block Marcus, Introduction to Philosophy, Slide 8

9 Token-Reflexiveness: A Problem P Time seems to outrun all possible utterances. P We might want to say meaningful things about the future that are not simultaneous with any utterance. P We can measure temporal distance from a current utterance. P But, we can not say anything about utterances simultaneous with such events. Marcus, Introduction to Philosophy, Slide 9

10 P Three things we might say: SN1: The sun will become a supernova, in the future. SN2: The sun is becoming a supernova, now. SN3: The sun became a supernova, in the past. P On the token reflexive approach we might understand SN1-3 as SNTR1-SNTR3. SNTR1. There is a time t such that the sun becomes a supernova at t and t is later than the utterance of SN1 (by some arbitrary measure of temporal distance). SNTR2. The sun becomes a supernova simultaneously with the utterance of SN2. SNTR3. There is a time t, such that the sun becomes a supernova at t, and t is earlier than the utterance of 3 (by some arbitrary measure of temporal distance). P SNTR.1 is fine. Supernova SN: The sun s becoming a supernova is future, will be present and then will be past. P SNTR.2-3 are false because there are no persons or utterances at the time of or after the supernova. Marcus, Introduction to Philosophy, Slide 10

11 A Solution P We might relativize all temporal claims to some claim, whether an utterance or an instance of a sentence, in the present. P In other words, we stick to measurements like SNTR.1. SNTR1. There is a time t such that the sun becomes a supernova at t and t is later than the utterance of SN1 (by some arbitrary measure of temporal distance). P Smart is not just translating A-theory sentences into B-theory sentences. P Some A-theory sentences will have to be eliminated altogether. P Put aside this problem for the token reflexive theory. Marcus, Introduction to Philosophy, Slide 11

12 The B-Theory and Eliminativism P The central claim of the B-theory is that we can do away with appeals to past, present, and future. P Zimmerman s presentist relies on claims about the exceptional nature of the present moment. Sentences about the past and future are legitimate because past, present, and future refer to intrinsic properties of events in respect of which events change. The A-theorist sees SN as ordinary and obvious. P The B-theorist denies that there is any such exception. The present is just one moment among many. The tenseless theory avoids parochial egocentrism. The B-theorist sees SN as ill-formed or nonsensical. Marcus, Introduction to Philosophy, Slide 12

13 Change and the A-Theory P For the A-theory, objects undergo changes as they become real by moving into the present. They become unreal by moving into the past. Object thus do not endure through time. P Smart believes that this aspect of the presentist view is implausible. A man or stone or star is commonly regarded as a three-dimensional object which nevertheless endures through time. This enduring through time clearly brings a fourth dimension into the matter... (94). Marcus, Introduction to Philosophy, Slide 13

14 Change and the B-Theory P The B-theorist s view of change may not be any more plausible. P Change is ordinarily thought of as an active process. P But, the B-theorist s view of change is static. Our notion of time as flowing, the transitory aspect of time..., is an illusion which prevents us seeing the world as it really is (94). P The B theorist must understand what we ordinarily take to be change as the comparison of different temporal slices of four-dimensional objects. When we think four-dimensionally...we replace the notions of change and staying the same by the notions of the similarity or dissimilarity of time slices of four-dimensional solids (95). P This static notion of change does not appear to be the ordinary notion, but Smart believes that it is better. The inability to translate talk of events changing in respect of pastness, presentness, and futurity into our tenseless language can be taken simply as a proof of the concealed token reflexivity of tenses and of words such as past, present, and future. Marcus, Introduction to Philosophy, Slide 14

15 The Rate of Time P Once we introduce change over time, we can start asking uncomfortable questions about the rate at which time passes. P Can time speed up or slow down? P Such questions, Smart believes, lead to an unintelligible infinite regress. We should need to postulate a hyper-time with reference to which our advance in time could be measured (seconds per hyper-seconds)... Moreover, anyone who thought that time-flow was necessary for time would presumably want to say that hyper-time-flow was necessary for hyper-time. He would therefore be driven to postulate a hyper-hyper-time, and so on without end (97). Marcus, Introduction to Philosophy, Slide 15

16 Taking Stock A-theory vs. B-theory P On the side of Zimmerman and the A-theorist Intuitions about the asymmetry of our access to the present moment and to past and future moments. The thank-goodness-that s-over feeling P On the side of Smart and the B-theorist The laws of physics express the ultimate nature of reality. In contrast, the terms of the A-theory are biased. The concepts of past, present, and future have significance relative only to human thought and utterance and do not apply to the universe as such. They contain a hidden anthropocentricity. So also do tenses. On the other hand, the concepts of earlier, simultaneous, and later are impeccably nonanthropocentric (94). P Every event is now at some time or another, and so the notion of now cannot be that of an objective property in nature which singles out some events from others (96). Marcus, Introduction to Philosophy, Slide 16

17 Translation P Smart urges us to translate away the A-theorists s uses of past, present, and future, by using constructions such as TR1-TR3. P But translations work in two directions. P One could try to reduce the B-relations to A-properties just as easily as we turn sentences referring to A-properties into ones invoking B-relations. P To counter that attempt, Smart introduces his fable of the king. Marcus, Introduction to Philosophy, Slide 17

18 The Fable of the King P In the imagined kingdom, the people recognize three classes of entities, alphas, betas, and gammas. Alphas are numbers less than the king s age. Betas are numbers equal to the king s age. Gammas are numbers greater than the king s age. P Every year, betas become alphas and gammas become betas. When the king turns twenty-six, say, the baseball team (which we would say has 25 members), which was Beta is now alpha. P Alphas, betas, and gammas are taken as primitive terms. P They could define our term number as anything that is either an alpha, a beta, or a gamma. Would this show that the notion of number had anything to do with the age of the king? It has indeed been introduced by reference to notions that have to do with the age of the king, but in such a way that this kingly reference cancels out (98). Marcus, Introduction to Philosophy, Slide 18

19 The Unimportance of Translation P Smart believes that our ability to define the B-terms in by using the A-terms does not show that the A-terms, like the king, have anything to do with the ultimate nature of time. P We must choose the scientific view. P I advocate my way, because it fits our ordinary way of talking much more closely to our scientific way of looking at the world and it avoids unnecessary mystification (99). Marcus, Introduction to Philosophy, Slide 19

20 Temporal Intuitions and Science P Recall that Zimmerman defends the A-theory by relying on our intuitions about the present. P Smart instead focuses on details of the construction of scientific theory. P It looks like we re contrasting philosophical intuition with science. Marcus, Introduction to Philosophy, Slide 20

21 Reflective Equilibrium Theory Evidence Marcus, Introduction to Philosophy, Slide 21

22 Philosophical Evidence P In science, the evidence is supposed to be observational. P In philosophy, the evidence is often intuitive. Many philosophical claims are modal, about necessity and possibility. We have no observational evidence of modality. P Intuitions are often the results of thought experiments. What if there were a sixth sense inaccessible to humans? What if we lived in a cave? What if we melted a piece of wax? What if we moved the universe over three inches or ahead ten minutes? What if there were another world just like ours except...? Marcus, Introduction to Philosophy, Slide 22

23 Philosophers on Intuitions P We do not mean a magical power or inner voice or special glow or any other mysterious quality. When you have an intuition that A, it seems to you that A... a genuine kind of conscious episode. (George Bealer). P The term intuition here is not being used in the sense of Spinoza, Bergson, or Husserl. It does not describe a cognitive act that is somehow superior to sensory perception. Nor, on the other hand, does it refer merely to hunches that are subsequently checkable by sensory perception or by calculation. Nor does this kind of intuition entail introspection, since it may just be implicit in a spoken judgment. Its closest analogue is an intuition of grammatical wellformedness. In short, an intuition that p is here just an immediate and untutored inclination, without evidence or inference, to judge that p (L. Jonathan Cohen). P We will call any judgment an intuitive judgment, or more briefly an intuition, just in case that judgment is not made on the basis of some kind of explicit reasoning process that a person can consciously observe (Alison Gopnik and Eric Schwitzgebel). P The Elephant and the Rider The elephant dwarfs the rider, who will have a hard time getting the elephant to do anything it doesn t want to. Still, one might think that the rider is basically in charge. Yet Haidt points out that the analytic system is a recent - and still somewhat buggy -evolutionary innovation, appended to a basically intuitive brain that previously managed pretty well without it... It s not that intuition is a tool that a rational creature often employs; it s rather, to put it crudely, that reason is a tool that a basically instinctual creature often employs to accomplish certain ends. For the most part, the intuitive system sets the agenda (Haybron). Marcus, Introduction to Philosophy, Slide 23

24 Science and Philosophy P A standard view: science proceeds empirically, from observation philosophy proceeds a priori, from intuitions P But proper scientific method is actually not empirical in the way that the standard view depicts. Marcus, Introduction to Philosophy, Slide 24

25 Galileo s Balls P Aristotle had claimed that a heavier body falls faster than a lighter one (H > L). But... P Consider a system consisting of the two bodies attached by a string. P The rate it falls is S. P Since, the light body falls more slowly than the heavier one, it should act as a drag on the system. So, S < H. P But, since the system is heavier than the single heavy body, it should fall more quickly. So S > H. P That s a contradiction. Marcus, Introduction to Philosophy, Slide 25

26 Evidence P In science, unlike in philosophy, evidence is supposed to be observational. P But, where is the evidence in Galileo s experiment? P Regarding the dropping of a rock on a ship (Galilean relativity): So, you have not made a hundred tests, or even one? And yet you so freely declare it to be certain?... Without experiment, I am sure that the effect will happen as I tell you, because it must happen that way (Galileo, Dialogue Concerning the Two Chief World Systems) Marcus, Introduction to Philosophy, Slide 26

27 Stevin s Chain Which way does the chain fall? Marcus, Introduction to Philosophy, Slide 27

28 Stevin s Solution (1605) P Unquestionably in the assumption from which Stevin starts, that the endless chain does not move, there is contained primarily only a purely instinctive cognition (Mach). Marcus, Introduction to Philosophy, Slide 28

29 Methods P In philosophy, unlike science, our evidence is not even supposed to be observational. P Traditionally, we rely essentially on intuitions, on the results of thought experiments. P This method has lately been derided as armchair philosophy. P In contrast, experimental philosophy is supposed to avoid some of the pitfalls of traditional methods. Marcus, Introduction to Philosophy, Slide 29

30 Business P Papers next Tuesday P Eternal Sunshine next Monday Same Time, Same Space Red Pit, 7pm P (Our third movie will be on a Wednesday.) Marcus, Introduction to Philosophy, Slide 30

Introduction to Philosophy Philosophy 110W Spring 2011 Russell Marcus

Introduction to Philosophy Philosophy 110W Spring 2011 Russell Marcus Introduction to Philosophy Philosophy 110W Spring 2011 Russell Marcus February 18 Smart, The Tenseless Theory of Time aka the B-Theory Marcus, Modern Philosophy, Spring 2010, Slide 1 The Presentist A-Theory

More information

The paradox of knowability, the knower, and the believer

The paradox of knowability, the knower, and the believer The paradox of knowability, the knower, and the believer Last time, when discussing the surprise exam paradox, we discussed the possibility that some claims could be true, but not knowable by certain individuals

More information

THE TENSELESS THEORY OF TIME. J.J.C. Smart

THE TENSELESS THEORY OF TIME. J.J.C. Smart THE TENSELESS THEORY OF TIME J.J.C. Smart B-THEORY AND INDEXICALS Answers Zimmermann s questions negatively. 1. There are not objective differences between past, present, and future 2. Present events are

More information

Paradoxes of special relativity

Paradoxes of special relativity Paradoxes of special relativity Today we are turning from metaphysics to physics. As we ll see, certain paradoxes about the nature of space and time result not from philosophical speculation, but from

More information

PROOF-THEORETIC REDUCTION AS A PHILOSOPHER S TOOL

PROOF-THEORETIC REDUCTION AS A PHILOSOPHER S TOOL THOMAS HOFWEBER PROOF-THEORETIC REDUCTION AS A PHILOSOPHER S TOOL 1. PROOF-THEORETIC REDUCTION AND HILBERT S PROGRAM Hilbert s program in the philosophy of mathematics comes in two parts. One part is a

More information

Comments on Markosian s How Fast Does Time Pass?

Comments on Markosian s How Fast Does Time Pass? Comments on Markosian s How Fast Does Time Pass? In 2 of his paper Markosian tries to spell out what he means to say when he says that time passes. Most of his discussion has to do with temporal language

More information

Russell s logicism. Jeff Speaks. September 26, 2007

Russell s logicism. Jeff Speaks. September 26, 2007 Russell s logicism Jeff Speaks September 26, 2007 1 Russell s definition of number............................ 2 2 The idea of reducing one theory to another.................... 4 2.1 Axioms and theories.............................

More information

Euler s Galilean Philosophy of Science

Euler s Galilean Philosophy of Science Euler s Galilean Philosophy of Science Brian Hepburn Wichita State University Nov 5, 2017 Presentation time: 20 mins Abstract Here is a phrase never uttered before: Euler s philosophy of science. Known

More information

Lecture 12: Arguments for the absolutist and relationist views of space

Lecture 12: Arguments for the absolutist and relationist views of space 12.1 432018 PHILOSOPHY OF PHYSICS (Spring 2002) Lecture 12: Arguments for the absolutist and relationist views of space Preliminary reading: Sklar, pp. 19-25. Now that we have seen Newton s and Leibniz

More information

Kripke on Frege on Sense and Reference. David Chalmers

Kripke on Frege on Sense and Reference. David Chalmers Kripke on Frege on Sense and Reference David Chalmers Kripke s Frege Kripke s Frege Theory of Sense and Reference: Some Exegetical Notes Focuses on Frege on the hierarchy of senses and on the senses of

More information

Critical Notice: Bas van Fraassen, Scientific Representation: Paradoxes of Perspective Oxford University Press, 2008, xiv pages

Critical Notice: Bas van Fraassen, Scientific Representation: Paradoxes of Perspective Oxford University Press, 2008, xiv pages Critical Notice: Bas van Fraassen, Scientific Representation: Paradoxes of Perspective Oxford University Press, 2008, xiv + 408 pages by Bradley Monton June 24, 2009 It probably goes without saying that

More information

To Infinity and Beyond. To Infinity and Beyond 1/43

To Infinity and Beyond. To Infinity and Beyond 1/43 To Infinity and Beyond To Infinity and Beyond 1/43 Infinity The concept of infinity has both fascinated and frustrated people for millennia. We will discuss some historical problems about infinity, some

More information

CS 361 Meeting 26 11/10/17

CS 361 Meeting 26 11/10/17 CS 361 Meeting 26 11/10/17 1. Homework 8 due Announcements A Recognizable, but Undecidable Language 1. Last class, I presented a brief, somewhat inscrutable proof that the language A BT M = { M w M is

More information

In a series of recent works, William Lane Craig attempts to provide a

In a series of recent works, William Lane Craig attempts to provide a Aporia vol. 24 no. 1 2014 The Direction of Time: A Focused Critique of an Argument for the Presentist Metaphysic In a series of recent works, William Lane Craig attempts to provide a comprehensive survey

More information

Hilbert and the concept of axiom

Hilbert and the concept of axiom Hilbert and the concept of axiom Giorgio Venturi Scuola Normale Superiore di Pisa Giorgio Venturi (SNS) Hilbert and the concept of axiom 1/24 First period Axiomatic method in the first period The actual

More information

Relations. Carl Pollard. October 11, Department of Linguistics Ohio State University

Relations. Carl Pollard. October 11, Department of Linguistics Ohio State University Department of Linguistics Ohio State University October 11, 2011 (Intuitive Idea) Intuitively, a relation is the kind of thing that either holds or doesn t hold between certain things. Examples: Being

More information

Ordinary Differential Equations Prof. A. K. Nandakumaran Department of Mathematics Indian Institute of Science Bangalore

Ordinary Differential Equations Prof. A. K. Nandakumaran Department of Mathematics Indian Institute of Science Bangalore Ordinary Differential Equations Prof. A. K. Nandakumaran Department of Mathematics Indian Institute of Science Bangalore Module - 3 Lecture - 10 First Order Linear Equations (Refer Slide Time: 00:33) Welcome

More information

Newton s First Law of Motion

Newton s First Law of Motion MATHEMATICS 7302 (Analytical Dynamics) YEAR 2017 2018, TERM 2 HANDOUT #1: NEWTON S FIRST LAW AND THE PRINCIPLE OF RELATIVITY Newton s First Law of Motion Our experience seems to teach us that the natural

More information

Discrete Mathematics for CS Fall 2003 Wagner Lecture 3. Strong induction

Discrete Mathematics for CS Fall 2003 Wagner Lecture 3. Strong induction CS 70 Discrete Mathematics for CS Fall 2003 Wagner Lecture 3 This lecture covers further variants of induction, including strong induction and the closely related wellordering axiom. We then apply these

More information

CS 124 Math Review Section January 29, 2018

CS 124 Math Review Section January 29, 2018 CS 124 Math Review Section CS 124 is more math intensive than most of the introductory courses in the department. You re going to need to be able to do two things: 1. Perform some clever calculations to

More information

ON MEREOLOGICAL ESSENTIALISM*

ON MEREOLOGICAL ESSENTIALISM* DISCUSSION ON MEREOLOGICAL ESSENTIALISM* ALVIN PLANTINGA PROFESSOR CHISHOLM'S PAPER is a powerful and probing effort to harmonize some conflicting philosophical intuitions about parts and wholes; but so

More information

MODAL LOGIC WITH SUBJUNCTIVE MARKERS: A NEW PERSPECTIVE ON RIGID DESIGNATION

MODAL LOGIC WITH SUBJUNCTIVE MARKERS: A NEW PERSPECTIVE ON RIGID DESIGNATION MODAL LOGIC WITH SUBJUNCTIVE MARKERS: A NEW PERSPECTIVE ON RIGID DESIGNATION Helge Rückert Department of Philosophy University of Saarbrücken, Germany Abstract: According to Kripke

More information

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 6 Length Contraction and Time Dilation (Refer Slide Time: 00:29) In our last lecture,

More information

Bell s spaceship paradox

Bell s spaceship paradox Bell s spaceship paradox If the two ships start accelerating at the same time, I always see them travelling at the same velocity, and keeping a constant distance... But I said the objects get shorter when

More information

Making Sense. Tom Carter. tom/sfi-csss. April 2, 2009

Making Sense. Tom Carter.   tom/sfi-csss. April 2, 2009 Making Sense Tom Carter http://astarte.csustan.edu/ tom/sfi-csss April 2, 2009 1 Making Sense Introduction / theme / structure 3 Language and meaning 6 Language and meaning (ex)............... 7 Theories,

More information

PHILOSOPHY OF PHYSICS (Spring 2002) 1 Substantivalism vs. relationism. Lecture 17: Substantivalism vs. relationism

PHILOSOPHY OF PHYSICS (Spring 2002) 1 Substantivalism vs. relationism. Lecture 17: Substantivalism vs. relationism 17.1 432018 PHILOSOPHY OF PHYSICS (Spring 2002) Lecture 17: Substantivalism vs. relationism Preliminary reading: Sklar, pp. 69-82. We will now try to assess the impact of Relativity Theory on the debate

More information

The Philosophy of Quantum Mechanics (Handout Eight) between the microphysical and the macrophysical. The macrophysical world could be understood

The Philosophy of Quantum Mechanics (Handout Eight) between the microphysical and the macrophysical. The macrophysical world could be understood The Philosophy of Quantum Mechanics (Handout Eight) 1. The Copenhagen Interpretation Bohr interpreted quantum theory as showing that there is a fundamental partition in nature, between the microphysical

More information

Williamson s Modal Logic as Metaphysics

Williamson s Modal Logic as Metaphysics Williamson s Modal Logic as Metaphysics Ted Sider Modality seminar 1. Methodology The title of this book may sound to some readers like Good as Evil, or perhaps Cabbages as Kings. If logic and metaphysics

More information

Indicative conditionals

Indicative conditionals Indicative conditionals PHIL 43916 November 14, 2012 1. Three types of conditionals... 1 2. Material conditionals... 1 3. Indicatives and possible worlds... 4 4. Conditionals and adverbs of quantification...

More information

Mathematical Logic Prof. Arindama Singh Department of Mathematics Indian Institute of Technology, Madras. Lecture - 15 Propositional Calculus (PC)

Mathematical Logic Prof. Arindama Singh Department of Mathematics Indian Institute of Technology, Madras. Lecture - 15 Propositional Calculus (PC) Mathematical Logic Prof. Arindama Singh Department of Mathematics Indian Institute of Technology, Madras Lecture - 15 Propositional Calculus (PC) So, now if you look back, you can see that there are three

More information

Journal of Theoretics Vol.5-3 Guest Commentary

Journal of Theoretics Vol.5-3 Guest Commentary Journal of Theoretics Vol.5-3 Guest Commentary The Nature of Time Frank Grimer f.grimer@grimer2.freeserve.co.uk The nature of time can best be appreciated by developing the concept of time from Information

More information

CS1800: Strong Induction. Professor Kevin Gold

CS1800: Strong Induction. Professor Kevin Gold CS1800: Strong Induction Professor Kevin Gold Mini-Primer/Refresher on Unrelated Topic: Limits This is meant to be a problem about reasoning about quantifiers, with a little practice of other skills, too

More information

The Philosophy of Physics. Is Space Absolute or Relational?

The Philosophy of Physics. Is Space Absolute or Relational? The Philosophy of Physics Lecture Two Is Space Absolute or Relational? Rob Trueman rob.trueman@york.ac.uk University of York Newton s Absolute Motion and Acceleration Is Space Absolute or Relational? Newton

More information

Mathematics-I Prof. S.K. Ray Department of Mathematics and Statistics Indian Institute of Technology, Kanpur. Lecture 1 Real Numbers

Mathematics-I Prof. S.K. Ray Department of Mathematics and Statistics Indian Institute of Technology, Kanpur. Lecture 1 Real Numbers Mathematics-I Prof. S.K. Ray Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Lecture 1 Real Numbers In these lectures, we are going to study a branch of mathematics called

More information

Intermediate Logic. Natural Deduction for TFL

Intermediate Logic. Natural Deduction for TFL Intermediate Logic Lecture Two Natural Deduction for TFL Rob Trueman rob.trueman@york.ac.uk University of York The Trouble with Truth Tables Natural Deduction for TFL The Trouble with Truth Tables The

More information

Ontology on Shaky Grounds

Ontology on Shaky Grounds 1 Ontology on Shaky Grounds Jean-Pierre Marquis Département de Philosophie Université de Montréal C.P. 6128, succ. Centre-ville Montréal, P.Q. Canada H3C 3J7 Jean-Pierre.Marquis@umontreal.ca In Realistic

More information

EASTERN DIVISION OF THE AMERICAN PHILOSOPHICAL ASSOCIATION 2009 GROUP MEETING: THE PHILOSOPHY OF TIME SOCIETY

EASTERN DIVISION OF THE AMERICAN PHILOSOPHICAL ASSOCIATION 2009 GROUP MEETING: THE PHILOSOPHY OF TIME SOCIETY EASTERN DIVISION OF THE AMERICAN PHILOSOPHICAL ASSOCIATION 2009 GROUP MEETING: THE PHILOSOPHY OF TIME SOCIETY PRESENTIST TIME TRAVEL AND THE LIMITS OF PRESENTIST CAUSALITY COMMENTATOR: MICHAEL NELSON UNIVERSITY

More information

CHAPTER 1. Introduction

CHAPTER 1. Introduction CHAPTER 1 Introduction A typical Modern Geometry course will focus on some variation of a set of axioms for Euclidean geometry due to Hilbert. At the end of such a course, non-euclidean geometries (always

More information

Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur

Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Modern Algebra Prof. Manindra Agrawal Department of Computer Science and Engineering Indian Institute of Technology, Kanpur Lecture 02 Groups: Subgroups and homomorphism (Refer Slide Time: 00:13) We looked

More information

Temporal Extension. 1. Time as Quantity

Temporal Extension. 1. Time as Quantity 1 Boris Hennig IFOMIS Saarbrücken Draft version as of July 17, 2005 Temporal Extension Abstract. Space and time are continuous and extensive quantities. But according to Aristotle, time differs from space

More information

Introduction to Philosophy Philosophy 110W Fall 2014 Russell Marcus

Introduction to Philosophy Philosophy 110W Fall 2014 Russell Marcus Introduction to Philosophy Philosophy 110W Fall 2014 Russell Marcus Class #8: Newton and Leibniz on Space and Time Marcus, Introduction to Philosophy, Fall 2014 Slide 1 Business P Return Exegeses P Thursday

More information

CH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction

CH 59 SQUARE ROOTS. Every positive number has two square roots. Ch 59 Square Roots. Introduction 59 CH 59 SQUARE ROOTS Introduction W e saw square roots when we studied the Pythagorean Theorem. They may have been hidden, but when the end of a right-triangle problem resulted in an equation like c =

More information

1.1 The Language of Mathematics Expressions versus Sentences

1.1 The Language of Mathematics Expressions versus Sentences The Language of Mathematics Expressions versus Sentences a hypothetical situation the importance of language Study Strategies for Students of Mathematics characteristics of the language of mathematics

More information

Instructor (Brad Osgood)

Instructor (Brad Osgood) TheFourierTransformAndItsApplications-Lecture26 Instructor (Brad Osgood): Relax, but no, no, no, the TV is on. It's time to hit the road. Time to rock and roll. We're going to now turn to our last topic

More information

Introducing Proof 1. hsn.uk.net. Contents

Introducing Proof 1. hsn.uk.net. Contents Contents 1 1 Introduction 1 What is proof? 1 Statements, Definitions and Euler Diagrams 1 Statements 1 Definitions Our first proof Euler diagrams 4 3 Logical Connectives 5 Negation 6 Conjunction 7 Disjunction

More information

First-Degree Entailment

First-Degree Entailment March 5, 2013 Relevance Logics Relevance logics are non-classical logics that try to avoid the paradoxes of material and strict implication: p (q p) p (p q) (p q) (q r) (p p) q p (q q) p (q q) Counterintuitive?

More information

ALBERT EINSTEIN AND THE FABRIC OF TIME by Gevin Giorbran

ALBERT EINSTEIN AND THE FABRIC OF TIME by Gevin Giorbran ALBERT EINSTEIN AND THE FABRIC OF TIME by Gevin Giorbran Surprising as it may be to most non-scientists and even to some scientists, Albert Einstein concluded in his later years that the past, present,

More information

30 Days to Awakening

30 Days to Awakening Formula for Miracles Presents 30 Days to Awakening Thousands of Years of Spiritual Wisdom Revealed in Fun, Ten Minute Insights 2012-2013 Brent Phillips www.formulaformiracles.net Day 25: Truth: Behind

More information

Discrete Structures Proofwriting Checklist

Discrete Structures Proofwriting Checklist CS103 Winter 2019 Discrete Structures Proofwriting Checklist Cynthia Lee Keith Schwarz Now that we re transitioning to writing proofs about discrete structures like binary relations, functions, and graphs,

More information

Simply Possible. Theodore Sider Philosophy and Phenomenological Research 60 (2000):

Simply Possible. Theodore Sider Philosophy and Phenomenological Research 60 (2000): Simply Possible Theodore Sider Philosophy and Phenomenological Research 60 (2000): 585 590 Abstract In the process of arguing against all theories of extended material objects made up of simples, Dean

More information

Philosophy 5340 Epistemology. Topic 3: Analysis, Analytically Basic Concepts, Direct Acquaintance, and Theoretical Terms. Part 2: Theoretical Terms

Philosophy 5340 Epistemology. Topic 3: Analysis, Analytically Basic Concepts, Direct Acquaintance, and Theoretical Terms. Part 2: Theoretical Terms Philosophy 5340 Epistemology Topic 3: Analysis, Analytically Basic Concepts, Direct Acquaintance, and Theoretical Terms Part 2: Theoretical Terms 1. What Apparatus Is Available for Carrying out Analyses?

More information

The nature of Reality: Einstein-Podolsky-Rosen Argument in QM

The nature of Reality: Einstein-Podolsky-Rosen Argument in QM The nature of Reality: Einstein-Podolsky-Rosen Argument in QM Michele Caponigro ISHTAR, Bergamo University Abstract From conceptual point of view, we argue about the nature of reality inferred from EPR

More information

The Philosophy of Physics. Special Relativity and Minkowski Spacetime

The Philosophy of Physics. Special Relativity and Minkowski Spacetime The Philosophy of Physics Lecture Five Special Relativity and Minkowski Spacetime Rob Trueman rob.trueman@york.ac.uk University of York Special Relativity a quick refresher Special Relativity and Minkowski

More information

The Converse of Deducibility: C.I. Lewis and the Origin of Modern AAL/ALC Modal 2011 Logic 1 / 26

The Converse of Deducibility: C.I. Lewis and the Origin of Modern AAL/ALC Modal 2011 Logic 1 / 26 The Converse of Deducibility: C.I. Lewis and the Origin of Modern Modal Logic Edwin Mares Victoria University of Wellington AAL/ALC 2011 The Converse of Deducibility: C.I. Lewis and the Origin of Modern

More information

What Does Quantum Mechanics Suggest About Our Perceptions of Reality?

What Does Quantum Mechanics Suggest About Our Perceptions of Reality? What Does Quantum Mechanics Suggest About Our Perceptions of Reality? Quantum mechanics suggests that we perceive at most a tiny sliver of reality. Of course we already knew that! We knew that the visible

More information

Two-Dimensional Modal Logic

Two-Dimensional Modal Logic Hardegree, Modal Logic, Chapter 10: Two-Dimensional Modal Logic 1 of 12 10 Two-Dimensional Modal Logic 1. Introduction...2 2. Scoped-Actuality...2 3. System 2D(1)...2 4. Examples of Derivations in 2D(1)...3

More information

Time and Change. Mc Taggart, Broad, Lowe, Smart, Prior: Problems, Difficulties, Hypotheses of Solutions

Time and Change. Mc Taggart, Broad, Lowe, Smart, Prior: Problems, Difficulties, Hypotheses of Solutions Time and Change. Mc Taggart, Broad, Lowe, Smart, Prior: Problems, Difficulties, Hypotheses of Solutions Michele Gentile 1. Introduction: Times as dimension of Change and Reality Abstract. This paper concerns

More information

Conceptual Explanations: Simultaneous Equations Distance, rate, and time

Conceptual Explanations: Simultaneous Equations Distance, rate, and time Conceptual Explanations: Simultaneous Equations Distance, rate, and time If you travel 30 miles per hour for 4 hours, how far do you go? A little common sense will tell you that the answer is 120 miles.

More information

Two-Dimensional Modal Logic

Two-Dimensional Modal Logic Hardegree, Modal Logic, 10: Two-Dimensional Modal Logic 13 X-1 10 Two-Dimensional Modal Logic 1. Introduction...2 2. Scoped-Actuality...2 3. System 2D(1)...3 4. Examples of Derivations in 2D(1)...4 5.

More information

CAUSATION CAUSATION. Chapter 10. Non-Humean Reductionism

CAUSATION CAUSATION. Chapter 10. Non-Humean Reductionism CAUSATION CAUSATION Chapter 10 Non-Humean Reductionism Humean states of affairs were characterized recursively in chapter 2, the basic idea being that distinct Humean states of affairs cannot stand in

More information

COPENHAGEN INTERPRETATION:

COPENHAGEN INTERPRETATION: QUANTUM PHILOSOPHY PCES 4.41 Perhaps the most difficult things to understand about QM are (i) how to reconcile our common sense ideas about physical reality with phenomena such as entanglement, & (ii)

More information

Chapter 4. Basic Set Theory. 4.1 The Language of Set Theory

Chapter 4. Basic Set Theory. 4.1 The Language of Set Theory Chapter 4 Basic Set Theory There are two good reasons for studying set theory. First, it s a indispensable tool for both logic and mathematics, and even for other fields including computer science, linguistics,

More information

Solar Energy Technology Prof. V. V. Satyamurty Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Solar Energy Technology Prof. V. V. Satyamurty Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Solar Energy Technology Prof. V. V. Satyamurty Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Evaluation of the Apparent Sunrise and Sunset Hour Angles (Refer

More information

Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay. Lecture - 15 Momentum Energy Four Vector

Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay. Lecture - 15 Momentum Energy Four Vector Special Theory of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 15 Momentum Energy Four Vector We had started discussing the concept of four vectors.

More information

Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras. Lecture - 13 Conditional Convergence

Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras. Lecture - 13 Conditional Convergence Real Analysis Prof. S.H. Kulkarni Department of Mathematics Indian Institute of Technology, Madras Lecture - 13 Conditional Convergence Now, there are a few things that are remaining in the discussion

More information

Presuppositions (introductory comments)

Presuppositions (introductory comments) 1 Presuppositions (introductory comments) Some examples (1) a. The person who broke the typewriter was Sam. b. It was Sam who broke the typewriter. c. John screwed up again. d. John likes Mary, too. e.

More information

Absolute motion versus relative motion in Special Relativity is not dealt with properly

Absolute motion versus relative motion in Special Relativity is not dealt with properly Absolute motion versus relative motion in Special Relativity is not dealt with properly Roger J Anderton R.J.Anderton@btinternet.com A great deal has been written about the twin paradox. In this article

More information

Introduction to Metalogic

Introduction to Metalogic Philosophy 135 Spring 2008 Tony Martin Introduction to Metalogic 1 The semantics of sentential logic. The language L of sentential logic. Symbols of L: Remarks: (i) sentence letters p 0, p 1, p 2,... (ii)

More information

A-Theory or B-Theory of Time? An Aristotelian Answer

A-Theory or B-Theory of Time? An Aristotelian Answer University of Windsor Scholarship at UWindsor Critical Reflections Essays of Significance & Critical Reflections 2017 Apr 1st, 1:15 PM - 1:45 PM A-Theory or B-Theory of Time? An Aristotelian Answer Luca

More information

Accuracy, Language Dependence and Joyce s Argument for Probabilism

Accuracy, Language Dependence and Joyce s Argument for Probabilism Accuracy, Language Dependence and Joyce s Argument for Probabilism Branden Fitelson Abstract In this note, I explain how a variant of David Miller s (975) argument concerning the language-dependence of

More information

Précis of Modality and Explanatory Reasoning

Précis of Modality and Explanatory Reasoning Précis of Modality and Explanatory Reasoning The aim of Modality and Explanatory Reasoning (MER) is to shed light on metaphysical necessity and the broader class of modal properties to which it belongs.

More information

Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur

Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur Structure of Materials Prof. Anandh Subramaniam Department of Material Science and Engineering Indian Institute of Technology, Kanpur Lecture - 5 Geometry of Crystals: Symmetry, Lattices The next question

More information

Math 38: Graph Theory Spring 2004 Dartmouth College. On Writing Proofs. 1 Introduction. 2 Finding A Solution

Math 38: Graph Theory Spring 2004 Dartmouth College. On Writing Proofs. 1 Introduction. 2 Finding A Solution Math 38: Graph Theory Spring 2004 Dartmouth College 1 Introduction On Writing Proofs What constitutes a well-written proof? A simple but rather vague answer is that a well-written proof is both clear and

More information

Alfred North Whitehead (English Mathematician and Philosopher; )

Alfred North Whitehead (English Mathematician and Philosopher; ) Artwork (cropped) from Shots of Awe YouTube series by Jason Silva Jason Silva (Venezuelan Media Artist, Futurist, Philosopher, 1982 - ) http://thisisjasonsilva.com/ Infinite Algebra Our minds are finite,

More information

CHAPTER 2. FORCE and Motion. CHAPTER s Objectives

CHAPTER 2. FORCE and Motion. CHAPTER s Objectives 19 CHAPTER 2 FORCE and Motion CHAPTER s Objectives To define a force To understand the relation between force and motion In chapter 1, we understood that the Greek philosopher Aristotle was the first who

More information

Solving Equations by Adding and Subtracting

Solving Equations by Adding and Subtracting SECTION 2.1 Solving Equations by Adding and Subtracting 2.1 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the addition property to solve equations 3. Determine whether

More information

Spacetime (Newtonian)

Spacetime (Newtonian) McTaggartʼs Denial of the Reality of Time Letʼs begin with a picture: Spacetime (Newtonian) The contents of a position in time [and I take T0, T1, etc. to be positions in time ] are called events. (458)

More information

240 Metaphysics. Frege s Puzzle. Chapter 26

240 Metaphysics. Frege s Puzzle. Chapter 26 240 Metaphysics Frege s Puzzle Frege s Puzzle 241 Frege s Puzzle In his 1879 Begriffsschrift (or Concept-Writing ), Gottlob Frege developed a propositional calculus to determine the truth values of propositions

More information

The rate of time's passage

The rate of time's passage The rate of time's passage Eric T. Olson 1. Many philosophers say that time has a kind of flow or passage that distinguishes it from space. Future times and events become less future; past ones become

More information

Quest Chapter 21. More heat energy means more of what type of energy? Does the mass change? So, what must change? What is the same in both containers?

Quest Chapter 21. More heat energy means more of what type of energy? Does the mass change? So, what must change? What is the same in both containers? 1 When a container of gas is heated, what happens to the average speed of its molecules? 1. Additional information is needed. 2. increases 3. doesn t change 4. decreases 2 (part 1 of 3) Two glasses of

More information

NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #2: Electrostatics. qq k r

NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #2: Electrostatics. qq k r NORTHRN ILLINOIS UNIVRSITY PHYSICS DPARTMNT Physics 11 &M and Quantum Physics Spring 018 Lab #: lectrostatics Lab Writeup Due: Mon/Wed/Thu/Fri, Jan. 9/31/Jan. 1/, 018 Background You ve learned a lot about

More information

HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science

HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science HPS 1653 / PHIL 1610 Introduction to the Philosophy of Science Laws of Nature Adam Caulton adam.caulton@gmail.com Wednesday 19 November 2014 Recommended reading Chalmers (2013), What is this thing called

More information

PROBLEMS OF CAUSAL ANALYSIS IN THE SOCIAL SCIENCES

PROBLEMS OF CAUSAL ANALYSIS IN THE SOCIAL SCIENCES Patrick Suppes PROBLEMS OF CAUSAL ANALYSIS IN THE SOCIAL SCIENCES This article is concerned with the prospects and problems of causal analysis in the social sciences. On the one hand, over the past 40

More information

8. Reductio ad absurdum

8. Reductio ad absurdum 8. Reductio ad absurdum 8.1 A historical example In his book, The Two New Sciences, 10 Galileo Galilea (1564-1642) gives several arguments meant to demonstrate that there can be no such thing as actual

More information

Math 300: Foundations of Higher Mathematics Northwestern University, Lecture Notes

Math 300: Foundations of Higher Mathematics Northwestern University, Lecture Notes Math 300: Foundations of Higher Mathematics Northwestern University, Lecture Notes Written by Santiago Cañez These are notes which provide a basic summary of each lecture for Math 300, Foundations of Higher

More information

Diodorus s Master Argument Nino B. Cocchiarella For Classes IC and IIC Students of Professor Giuseppe Addona

Diodorus s Master Argument Nino B. Cocchiarella For Classes IC and IIC Students of Professor Giuseppe Addona Diodorus s Master Argument Nino B. Cocchiarella For Classes IC and IIC Students of Professor Giuseppe Addona In my Remarks on Stoic Logic that I wrote for you last year, I mentioned Diodorus Cronus s trilemma,

More information

Commentary on Guarini

Commentary on Guarini University of Windsor Scholarship at UWindsor OSSA Conference Archive OSSA 5 May 14th, 9:00 AM - May 17th, 5:00 PM Commentary on Guarini Andrew Bailey Follow this and additional works at: http://scholar.uwindsor.ca/ossaarchive

More information

Vocabulary atom atomos Dalton's atomic theory law of constant composition law of definite proportions law of multiple proportions matter.

Vocabulary atom atomos Dalton's atomic theory law of constant composition law of definite proportions law of multiple proportions matter. 1.3 Early Atomic Theory Lesson Objectives The student will: define matter and explain how it is composed of building blocks known as atoms. give a short history of how the concept of the atom developed.

More information

On an Unsound Proof of the Existence of Possible Worlds

On an Unsound Proof of the Existence of Possible Worlds 598 Notre Dame Journal of Formal Logic Volume 30, Number 4, Fall 1989 On an Unsound Proof of the Existence of Possible Worlds CHRISTOPHER MENZEL* Abstract In this paper, an argument of Alvin Plantinga's

More information

PREAMBLE (Revised) Why Einstein was Mistaken About the Velocity of Light.

PREAMBLE (Revised) Why Einstein was Mistaken About the Velocity of Light. PREAMBLE (Revised) Why Einstein was Mistaken About the Velocity of Light. Einstein s 1905 Special Theory of Relativity is primarily about the velocity of a ray of light after it is emitted from a material

More information

MITOCW watch?v=0usje5vtiks

MITOCW watch?v=0usje5vtiks MITOCW watch?v=0usje5vtiks PROFESSOR: Mach-Zehnder-- interferometers. And we have a beam splitter. And the beam coming in, it splits into 2. A mirror-- another mirror. The beams are recombined into another

More information

Part I Electrostatics. 1: Charge and Coulomb s Law July 6, 2008

Part I Electrostatics. 1: Charge and Coulomb s Law July 6, 2008 Part I Electrostatics 1: Charge and Coulomb s Law July 6, 2008 1.1 What is Electric Charge? 1.1.1 History Before 1600CE, very little was known about electric properties of materials, or anything to do

More information

Figure 1: Doing work on a block by pushing it across the floor.

Figure 1: Doing work on a block by pushing it across the floor. Work Let s imagine I have a block which I m pushing across the floor, shown in Figure 1. If I m moving the block at constant velocity, then I know that I have to apply a force to compensate the effects

More information

Some Writing Examples

Some Writing Examples Some Writing Examples Assume that A : ( A = n = x, y A : f(x) = f(y)). Let B = n + 1, x, y B, x y, C := B \ {y}, D := B \ {x}. C = n, D = n, x C, y D. Let u B, u x, u y. u C, f(x) = f(u), u D, f(y) = f(u),

More information

More on infinite series Antiderivatives and area

More on infinite series Antiderivatives and area More on infinite series Antiderivatives and area September 28, 2017 The eighth breakfast was on Monday: There are still slots available for the October 4 breakfast (Wednesday, 8AM), and there s a pop-in

More information

Handout 8: Bennett, Chapter 10

Handout 8: Bennett, Chapter 10 Handout 8: Bennett, Chapter 10 Philosophy 691: Conditionals Northern Illinois University Fall 2011 Geoff Pynn terminology 1. Chapters 10-18 concern subjunctive conditionals, which Bennett distinguishes

More information

Introduction to Bayesian Statistics and Markov Chain Monte Carlo Estimation. EPSY 905: Multivariate Analysis Spring 2016 Lecture #10: April 6, 2016

Introduction to Bayesian Statistics and Markov Chain Monte Carlo Estimation. EPSY 905: Multivariate Analysis Spring 2016 Lecture #10: April 6, 2016 Introduction to Bayesian Statistics and Markov Chain Monte Carlo Estimation EPSY 905: Multivariate Analysis Spring 2016 Lecture #10: April 6, 2016 EPSY 905: Intro to Bayesian and MCMC Today s Class An

More information

The World According to Wolfram

The World According to Wolfram The World According to Wolfram Basic Summary of NKS- A New Kind of Science is Stephen Wolfram s attempt to revolutionize the theoretical and methodological underpinnings of the universe. Though this endeavor

More information

GALILEAN RELATIVITY. Projectile motion. The Principle of Relativity

GALILEAN RELATIVITY. Projectile motion. The Principle of Relativity GALILEAN RELATIVITY Projectile motion The Principle of Relativity When we think of the term relativity, the person who comes immediately to mind is of course Einstein. Galileo actually understood what

More information

Syllogistic Logic and its Extensions

Syllogistic Logic and its Extensions 1/31 Syllogistic Logic and its Extensions Larry Moss, Indiana University NASSLLI 2014 2/31 Logic and Language: Traditional Syllogisms All men are mortal. Socrates is a man. Socrates is mortal. Some men

More information